Inflatable ball for footballing and recreational activities

ABSTRACT

This invention relates to an inflatable ball ( 1 ) for footballing and recreational activities. It is based on a new geometric model. It considers the use of unrolled folding curved surfaces—cylindrical surfaces—to create spherical three-dimensional structures—domes and geoids—to replace the current structures that make use of plane geometrical figures such as the truncated icosahedron. It is a configuration that corresponds to a ball ( 1 ) with 12 faces or panels ( 2 ), 24 edges ( 3 ) and 14 vertices, six are type (A) and eight are type (B), which takes advantage of the curvature of solids to replicate a warped, spherical figure and moulds are not needed to make them. That is, with the advantage that it can be made based on development of surfaces.

FIELD OF INVENTION

1. Technical Area to Which the Invention Belongs

This invention relates to an inflatable ball (1) for footballing andrecreational activities, and therefore hollow, that can be used in anyarea where balls are used: sports, culture and science.

2. State of the Art

This invention relates to an inflatable ball (1) for footballing andrecreational activities. It is based on a new geometric model suitablefor building spherical three-dimensional structures. Even though it haspotential for use in areas such as the building industry, this inventionhas been developed with a view to producing inflatable balls forfootballing and recreational purposes.

According to FIFA the first footballs of the modern era, so calledbecause they were specifically designed and made to be used in games,appeared at the end of the 19^(th) century, under the rules devised bythe first football association, formed in England on 26 Oct. 1863.

The geometry of the balls, made from tanned leather and ox bladder,resembled that of the Earth. They consisted of panels stitched together.They were wider at the equator and narrowed towards the poles.

The first major improvement was a geometric adjustment to the shape. Asthe inflation system improved, with a rubber air chamber, it could keepits round shape for longer. This model to some extent resembled today'svolleyball balls. It was basically composed of 18 faces or panels andwas officially in use until 1966 when it was replaced by a ball ofsimilar geometry, but better made, to comply with the strictrequirements of FIFA to be considered the ‘official ball’.

1970 saw the launch of the first ‘truncated icosahedron’ model, whichhas lasted until the present day. Major changes have been made sincethen: not in the format of the ball but in the quality of the materialsand construction systems, which have systematically led to the ballbecoming a tough, ergonomic object.

The World Cup competitions, in addition to demanding quality guarantees,have also served as a laboratory for introducing increasinglysophisticated products.

Models were launched in Germany (2006) and South Africa (2010) whosesurface geometry differed from their predecessor. However, given themanufacturing process of the official ball for the last tournament it isverifiable that the icosahedric shape persists in the interior.Differences are seen in the layers of the covering, designed to enhancethe object's performance.

The football-making process is today divided into two, duly patented,aspects: materials, and geometry.

The materials have seen more developments and experimentation in recenttimes, the aim being to unite the functionality requirements ofroundness, bounce and rebound with the toughness and durabilityrequirements under use, such as surface impermeability, suitability tothe pitch covering, resistance to wear, and other aspects beyond thescope of this invention.

The geometric aspect has not changed since 1970, with the use of aninflated truncated icosahedron (one of the 13 Archimedean solids) torepresent a spherical dome. Occasional experiments have been tried withother shapes, but they used moulds on the traditional geometric model.

This invention is intended to contribute to that aspect.

SUMMARY OF INVENTION

This invention relates to an inflatable ball (1) for footballing andrecreational activities. It is based on a new geometric model. Itconsiders the use of unrolled folding curved surfaces—cylindricalsurfaces—to create spherical three-dimensional structures—domes andgeoids—to replace the current structures that make use of planegeometrical figures such as the truncated icosahedron. It is aconfiguration that corresponds to a ball (1) with 12 faces or panels(2), 24 edges (3) and 14 vertices (intersections of the edges), six aretype (A), ends of segment nr/2 (5), and eight are type (B), ends ofsegment r√{square root over (2)} (4), which takes advantage of thecurvature of solids to replicate a warped, spherical figure withoutneeding to use moulds. That is, with the advantage of being made basedon development of surfaces.

DETAILED DESCRIPTION OF THE INVENTION

This invention is a ball (1) suitable for footballing and recreationalactivities, composed of 12 faces or panels (2), which are reflected onthe surface of the ball (1), each corresponding to sections ofcylindrical surfaces, that is, unrolled folding curved surfaces.

In practice, when the twelve faces or panels (2) of the ball (1), whichare quadrilateral in shape and all equal, are arranged with differentorientations they form a three-dimensional structure with a sphericalformat.

The ball (1) may thus be described as a geometric figure, aNon-polyhedron, composed of 12 faces or panels (2), 24 edges (3) and 14vertices, six of type (A) and eight of type (B),

The advantage of adapting this geometric figure to a sphere is that,because it has fewer cylindrical faces or panels, and a smaller numberof vertices (compared with the previous model—inflated truncatedicosahedrons), there are fewer areas that have to be inflated, and it iseasier to achieve the desired outcome: the ball (1). The cumulativestress in the vertices can be distributed along the edges and thence itis transmitted equally to all the faces or panels.

The invention thus comprises of an inflatable ball for footballing andrecreational activities composed of an inner air chamber and outercovering formed by 12 all equal quadrilateral faces or panels (2), witheach panel (2) bounded by 4 edges (3) of equal length by which thepanels are joined to one another. Each panel (2) is bounded on itscircumference by four other panels (2).

The panels (2) have a curved surface due to their being superimposed ona Non-polyhedron composed of 12 faces or panels (2), 24 edges (3) and 14vertices, six of type (A) and eight of type (B), yielded by theintersection of three cylinders of equal diameter (d=22 cm) where eachof its axes establishes, in the space, an angle of 90°, oriented alongthe xx, yy and zz orthonormal axes whose faces or panels are all equaland correspond to portions of a cylinder.

The panels (2) are bounded by 4 edges (3) which, since they result fromthe intersection of three cylinders with orthonormal axes of equaldiameter, correspond to sections of an ellipse, whose smaller axis is r(radius of the cylinder), 11 cm, and larger axis is r √{square root over(2)}, dimension between 15.55 cm and 15.56 cm, when converted todecimals, since the intersection between each pair of cylinders is 45°.

The panels (2) are doubly symmetrical plane geometric figures, both inrelation to segment nr/2 (5), which corresponds to one quarter of thecircumference of the base of the cylinder, and in relation to thesegment r√{square root over (2)} (4) which corresponds to the portion ofthe generating line that passes through the mid-point of the previoussegment, which intersects it also at its mid-point, and whichcorresponds to the maximum moment of this magnitude, equal to twice thecosine of 45°, angle at which each pair of cylinders intersects. Eachpanel has four opposing vertices, two type (A), ends of the segment nr/2(5), and two type (B), ends of the segment r√{square root over (2)} (4).The area of each panel (2) is between 160.70 cm² and 160.80 cm², itsperimeter is between 47.00 linear cm and 47.30 linear cm, making between1928.40 cm² and 1929.60 cm² of material; and between 2256.00 cm and2270.40 cm of outline necessary for joining according to the vertices ofeach end of the ellipse portion: (A) to (A) and (B) to (B).

The panels (2) thus correspond to the joining of four faces or panels onvertex (A), with tessellation [4,4,4,4], and the joining of three facesor panels on vertex (B), with tessellation [4,4,4], seeing tessellationas the splitting of the area into regions.

Each edge (3) is delimited at 45°, with the least pronounced curveprevailing, and it is supported on a vertex that corresponds to the endsof two orthogonal segments which intersect at the mid-point, where thefirst (4) measures r√{square root over (2)}, a dimension between 15.55cm and 15.56 cm, and the second (5), given by the unrolling of thecircumference portion, measures nr/2, a dimension between 17.27 cm and17.28 cm, after the surface development of each panel.

Each edge (3) thus corresponds to a portion of an ellipse that issupported on two vertices, where the end of the ellipse portioncorresponding to the point above the smaller axis is supported on thevertex (A) of the segment nr/2 (5), and the end of the ellipse sectionedby the planes at 45° corresponds to the vertex (B) of the segmentr√{square root over (2)} (4).

Each edge (3) is between 11.80 cm and 11.85 cm long, and when joined twoby two they yield a stitched area of 283.20 cm to 284.40 cm, which joinsall the panels (2).

There are basically three advantages of using this new geometric form:

-   -   1—smaller number of ball (1) components, from:        -   32 faces or panels, 90 edges and 60 vertices (truncated            icosahedrons), to:        -   12 faces or panels (2), 24 edges (3) and 14 vertices, six of            type (A) and eight of type (B), (proposed Non-polyhedron).        -   As it is made of fewer faces or panels (2), which are larger            and all the same, and evenly distributed, the result is a            more balanced shape that is easier to assemble, yielding an            object with reduced friction and better performance.    -   2—current manufacturing processes can be easily adapted to this        geometry. Since this model comprises unrolled faces or panels        (2), all that is needed is for the moulds to be adapted to the        cutting proposed herein. There is no need to alter the assembly        routine or use any other equipment.    -   3—lower production cost and less wastage. As the object is        composed of quadrilateral faces or panels (2) repeating them        takes better advantage of the cutting area of the mould, leading        to less wastage of the raw material, from 40% or more to 12%,        compared with cutting a ball of the kind currently produced. As        a result, better management of the material used is anticipated,        including the arrangement of the decorative motifs to be printed        on the roll of material. It is estimated that 30% less stitching        is needed than with present patterns: from:        -   (90 edges×4.5 cm)=405 cm (truncated icosahedron), to:        -   (24 edges (3)×11.8 cm)=283.2 cm (proposed Non-polyhedron).

So we can conclude that the product described could successfully replaceits predecessors.

DESCRIPTION OF THE FIGURES

FIG. 1 shows the structure of the ball (1).

FIG. 2 shows the ball (1) created by inflating the proposedNon-polyhedron.

FIG. 3 shows the proposed Non-polyhedron.

FIG. 4 represents the creation of the proposed Non-polyhedron, by theintersection of three cylinders of equal diameter and with orthonormalaxes between them.

FIG. 5 shows the intersection, the bearing (European Method), and thetrue shape of the edge (3) from the proposed Non-polyhedron.

FIG. 6 shows the surface development of the face or panel (2) created bythe proposed Non-polyhedron.

FIG. 7 shows the construction of the ball (1), showing the joining ofthe panels (2) of the proposed Non-polyhedron.

FIG. 8 shows an arrangement for cutting the panels (2).

REFERENCES

CRITCHLOW, K. 1973. Order in Space. A Design Source Book, Thames andHudson, London. ISBN 0500340331

MURANI, C., 2004. “A Tesselação (5,6,6)—A Bola de Futebol—Visualizada emCaleidoscópio Generalizado”. Anais do VIII Encontro Nacional de EducaçãoMatemática, Educação Matemática: Um Compromisso Social, ComunicaçãoCientifica GT 3—Educação Matemática no Ensino Médio, UniversidadeFederal de Pernambuco, Recife, 18 to 15 July.

PRICE, D. S., JONES, R., HARLAND, A. R., ‘Soccer ball anisotropymodelling’, Materials Science and Engineering, Elsevier, 2006(doi:10.1016/j.msea.2006.01.079)

RELATED PATENTS

European Patent—652794—Inflatable Ball for Ball Games, in particularFootball—Jul. 9, 1993—A63B 41/08 (2006.01)

European Patent—946230—A Football Teaching Aid—Oct. 15, 1997—A63B 69/00(2006.01)

European Patent—598542—Inflatable Sports Ball—Nov. 9, 1993—A63B 41/08(2006.01)

(WO2004056424) BALL FOR BALL GAME AND METHOD FOR MANUFACTURING THE SAME

Hollow inflatable balls (connecting valves to inflatable elastic bodiesB60C29/00; valves, e.g. self-closing valves F16K) A63B41

Date: Dec. 16, 2011.

1. Inflatable ball (1) for footballing and recreational activitiescomprising an inner air chamber and an outer covering formed by multiplepanels, said outer covering being composed of 12 panels (2),quadrilateral in shape and all identical, with each panel (2) beingdelimited by four edges (3) of equal length through which said panelsare joined together, with each panel (2) circumferentially bounded byfour other panels, each said panel (2) having a curved surface resultingfrom the overlay of a Non-polyhedron comprising of 12 faces or panels(2), 24 edges (3) and 14 vertices, six of type (A) and eight of type(B), yielded by the intersection of three cylinders of equal diameter,22 cm, each of whose axes establishes, in the space, an angle of 90°,oriented along the xx, yy and zz orthonormal axes whose faces or panels(2) are all equal and correspond to portions resulting from theintersection of the aforementioned cylinders.
 2. Inflatable ball (1) forfootballing and recreational activities, according to claim 1, whereinsaid panels (2) are bounded by four edges (3) which, since they resultfrom the intersection of three cylinders with equal diameter andorthonormal axes, correspond to portions of an ellipse, whose smalleraxis is r, measuring 11 cm, and larger axis is r√2, a dimension between15.55 cm and 15.56 cm.
 3. Inflatable ball (1) for footballing andrecreational activities, according to the preceding claims, wherein saidpanels (2) correspond to doubly symmetrical plane geometric figures,both in relation to the segment nr/2 (5) and in relation to the segmentr√2 (4).
 4. Inflatable ball (1) for footballing and recreationalactivities, according to the preceding claims, wherein said panels (2)contain four vertices, opposing to each other, two type (A) and two type(B).
 5. Inflatable ball (1) for footballing and recreational activities,according to the preceding claims, wherein each of said panels (2) hashave an area between 160.70 cm² and 160.80 cm², with a perimeter between47.00 linear cm and 47.30 linear cm, making between 1928.40 cm² and1929.60 cm² of material and between 2256.00 cm and 2270.40 cm of outlinenecessary for joining according to the vertices of each end of ellipseportion: (A) to (A) and (B) to (B).
 6. Inflatable ball (1) forfootballing and recreational activities, according to the precedingclaims, wherein said panels (2), correspond to the joining of four facesor panels (2) on vertex (A), with tessellation [4,4,4,4], and thejoining of three faces or panels (2) on vertex (B), with tessellation[4,4,4].
 7. Inflatable ball (1) for footballing and recreationalactivities, according to the preceding claims, wherein each edge (3) isdelimited at 45°, with the least pronounced curve prevailing. 8.Inflatable ball (1) for footballing and recreational activities,according to the preceding claims, wherein each edge (3) is supported ona vertex that corresponds to the ends of two orthogonal segments whichintersect on its mid-point, where the first (4) measures r√2, adimension between 15.55 cm and 15.56 era, and the second (5), given bythe unrolling of the circumference portion, measures nr/2, a dimensionbetween 17.27 cm and 17.28 cm, after the surface development of eachpanel.
 9. Inflatable ball (1) for footballing and recreationalactivities, according to the preceding claims, wherein each edge (3)corresponds to a portion of an ellipse that is supported on twovertices, where the end of the ellipse portion corresponding; to thepoint above the smaller axis is supported on the vertex (A) of thesegment nr/2 (5), and the end of the ellipse sectioned by the planes at45° corresponds to the vertex (B) of the segment r√2 (4).
 10. Inflatableball (1) for footballing and recreational activities, according to thepreceding claims, wherein each edge (3) is between 11.80 cm and 11.85 cmlong, and when joined two by two they yield a stitched area of 283.20 cmto 283.40 cm, which joins all the panels (2).